Session C10: Invited Session: Stabilization and Dynamics of Magnetic Skyrmions

Emergent Electrodynamics of Skyrmions in Chiral Magnets

Skyrmions are particle-like states of continuous fields named after the English particle physicist Tony Skyrme. Their existence has long been considered in nuclear matter, quantum Hall systems, liquid crystals, superfluid $^3$He and ultracold atoms. As their defining property they support a topological winding number of 1. In magnetic materials spin configurations with a non-vanishing topological winding number, driven by the interplay of magnetic anisotropies, dipolar interactions and geometrical frustration, have been known for a long time. This is contrasted by the recent discovery of skyrmion lattices in chiral magnets, i.e., long-range magnetic order in which each magnetic unit cell contains a skyrmion and thus a non-zero winding number. As a practical consequence, the non-zero topological winding number implies that the conduction electrons in the presence of a skyrmion experience changes of Berry phase, that correspond precisely to one quantum of emergent magnetic flux. In transport measurements this leads directly to a topological Hall signal. Moreover, tiny electric current densities are already sufficient to generate a motion of the skyrmions first observed indirectly in neutron scattering. Since each skyrmion supports one quantum of emergent magnetic flux the motion of the skyrmions induces an emergent electric field consistent with Faradays law of induction that may also be observed experimentally. The excellent theoretical description of the skyrmion lattices observed so far in metals, doped semiconductors and insulators suggests that they represent a rather universal phenomenon to be expected in a wide range of systems supporting chiral spin interactions. Taken together with the first insights into their emergent electrodynamics, skyrmion lattices in chiral magnets develop into a new area of condensed matter magnetism offering insights relevant for applications.   

Extended skyrmion phase in epitaxial FeGe(111) thin films

Exotic magnetic skyrmions with a new type of topological spin texture have recently been observed in cubic B20 magnets such as MnSi and FeGe [1]. Skyrmions, with a double-twist spin texture carrying a topological charge and a Berry phase in real space, can form long-range ordered structure or behave as solitons [2]. These magnetic skyrmions not only provide a novel route to study the topological nature of magnetic defects but also exhibit spectacular static and dynamic properties such as translational and rotational motion driven by electric current with ultra-low current density. Unfortunately, the skyrmion phase in bulk crystals exists only in a very small region of a few K and a narrow magnetic field range in the phase space. However, theories and some experiments suggest that the skyrmion phase may be greatly expanded in thin films. In this work, we describe the realization of B20 FeGe thin films with greatly expanded skyrmion phase [3]. FeGe has the highest Curie temperature $T_{C} \approx $ 280 K among the B20 skyrmion materials, but FeGe crystals rarely exceed 1 mm. We have succeeded in the epitaxial growth of FeGe(111) thin films on Si(111). We show that the skyrmion states, as revealed by the topological Hall effect and the small angle neutron scattering (SANS), are stabilized in a dramatically larger region in phase space in FeGe films, including the entire temperature range up to $T_{C}$, and in a large field range. Furthermore, the properties of the skyrmion phase can be controlled and manipulated by the film thickness. Other aspects of the skyrmion states as revealed by transport and neutron measurements will also be discussed. This work is in collaboration with C. L. Chien and C. Broholm at JHU and L. Debeer-Schmitt and K. Littrell at ORNL. \\[4pt] [1] S. M\"{u}hlbauer\textit{ et al.}, Science \textbf{323}, 915 (2009); X. Z. Yu\textit{ et al.}, Nat Mater. 10, 106 (2011).\\[0pt] [2] U. K. R\"{o}{\ss}ler \textit{et al.}, J. Phys.Conf. Ser. 303, 012105 (2011).\\[0pt] [3] S. X. Huang, and C. L. Chien, Phys. Rev. Lett. \textbf{108}, 267201 (2012).   

Realization and dynamics of 2D magnetic skyrmions

The skyrmion, a vortex-like topological spin texture, can be excited by the external magnetic field (B) in helimagnets [1-6]. The skyrmion lattice was recently confirmed by small-angle scattering neutron observations in a helimagnet MnSi [1] where the skyrmion phase was observed in a narrow window of (T, B)-plane. In contrast with unstable skyrmions in the bulk, by using Lorentz transmission electron microscopy (TEM), we have realized two-dimensional (2D) skyrmion crystal (SkX) over a wider region in (T, B)-plane for thin helimagnets [2-6] which thicknesses are smaller than their helical periods. Furthermore, we have realized the near RT ($\sim$280 K) formation of SkX in a helimagnet FeGe [3]. We have clarified the stability condition for the SkX, i.e. the magnetic-dimension (from 2D to 3D) variation of SkX phase diagram in (T, B)-plane. The skyrmion acts as a magnetic flux owing to its curved spin texture. When an electric current flowing through the skyrmion exceeds a critical current density for depinning, the skyrmion can accept the spin transfer torque to be driven along the current direction. Combining electrical and magnetic control in a microdevice composed of a FeGe thin plate, we have realized nanometric skyrmions under a weak magnetic field (150 mT) and manipulated them with an ultra-low current density ($\sim$ 5 $\times$ 10$^{4}$A/m$^{2})$ [6], several orders lower than that required to drive domain walls in conventional ferromagnets [7]. This work has been done in collaboration with Prof. Y. Tokura, Prof. N. Nagaosa, Dr. Y. Matsui, Prof. Y. Onose, Mr. N. Kanazawa, Dr. K. Kimoto, Dr. T. Hara, Dr. T. Nagai, and Ms. W-Z. Zhang. \\[4pt] [1] S. M\"uhlbauer, \textit{et al}., \textbf{Science} \textbf{323}, 915 (2009)\\[0pt] [2] X.Z. Yu, \textit{et al.}, \textit{Nature} \textbf{465}, 901 (2010)\\[0pt] [3] X.Z. Yu, \textit{et al}., \textit{Nat. Mater. }\textbf{10}, 106 (2011)\\[0pt] [4] S. Seki, \textit{et al}., \textit{Science} \textbf{336}, 198 (2012)\\[0pt] [5] A. Tonomura, \textit{et al}. \textit{Nano Lett.} \textbf{102}, 186602 (2012)\\[0pt] [6] X.Z. Yu, \textit{et al}., \textit{Nat. Commun.}, \textbf{3}:988(2012) \\[0pt] [7] S. Parkin, \textit{et al}., \textit{Science}, \textbf{320}, 190 (2008)   

Beller Lectureship: Dynamics of skyrmions under electric current

Current-driven motion of the skyrmions and skyrmion crystal is attracting intense attention because of the very small critical current density, but the microscopic mechanism of their motion is not yet explored. In this talk, I will present a numerical simulation of the Landau-Lifshitz-Gilbert (LLG) equation and an analytic theory, which reveals a remarkably robust and universal current-velocity relation of the skyrmion motion driven by the spin transfer torque unaffected by either impurities or nonadiabatic effect in sharp contrast to the case of domain wall or spin helix. This is due to the peculiar dynamics of skyrmions characterized by inherent absence of the intrinsic pinning and flexible shape-deformation of skyrmions so as to avoid pinning centers. The effect of the constricted geometry will be also discussed. This work has been done in collaboration with J. Iwasaki and M. Mochizuki.   

Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions

Skyrmions are topologically protected field configurations with particle-like properties that play an important role in various fields of science. They have been predicted to exist also in bulk magnets and in recent experiments it was shown that they can be induced by a magnetic field. A key ingredient for their occurrence is the Dzyaloshinskii-Moriya interaction (DMI) which was found to be strong also for magnetic nanostructures on substrates with large spin-orbit coupling [1]. In these systems the DMI stabilizes spin-spirals with a unique rotational sense propagating along one direction of the surface as observed for ultrathin films [1-3] and atomic chains [4]. Here, we go a step beyond and present an atomic-scale skyrmion lattice as the magnetic ground state of a hexagonal Fe monolayer on Ir(111) [5]. We develop a spin-model based on density functional theory that explains the interplay of Heisenberg exchange, DMI and the four-spin exchange as the microscopic origin of this intriguing magnetic state. Experiments using spin-polarized scanning tunneling microscopy confirm the skyrmion lattice which is incommensurate with the underlying atomic lattice. This work is a collaboration with G. Bihlmayer, S. Bl\"ugel, K. von Bergmann, M. Menzel, A. Kubetzka, J. Brede, and R. Wiesendanger. \\[4pt] [1] M. Bode et al., Nature 447, 190 (2007). \\[0pt] [2] P. Ferriani et al., Phys. Rev. Lett. 101, 027201 (2008).\\[0pt] [3] Y. Yoshida et al., Phys. Rev. Lett. 108, 087205 (2012).\\[0pt] [4] M. Menzel el al., Phys. Rev. Lett. 108, 197204 (2012).\\[0pt] [5] S. Heinze et al., Nature Phys. 7, 713 (2011).